Level set topology of the nuclear charge space and the electronic energy functional

1982 ◽  
Vol 22 (1) ◽  
pp. 101-114 ◽  
Author(s):  
Paul G. Mezey
Keyword(s):  
Level Set ◽  
Nuclear Charge ◽  
Energy Functional ◽  
Electronic Energy ◽  
Charge Space

scholarly journals On the Relationship between Variational Level Set-Based and SOM-Based Active Contours

2015 ◽  
Vol 2015 ◽  
pp. 1-19 ◽  
Author(s):  
Mohammed M. Abdelsamea ◽  
Giorgio Gnecco ◽  
Mohamed Medhat Gaber ◽  
Eyad Elyan
Keyword(s):  
Level Set ◽  
Active Contour ◽  
Active Contours ◽  
Level Set Methods ◽  
Energy Functional ◽  
Self Organizing Maps ◽  
Complex Shapes ◽  
Variational Level Set ◽  
Preservation Property ◽  
The Relationship

Most Active Contour Models (ACMs) deal with the image segmentation problem as a functional optimization problem, as they work on dividing an image into several regions by optimizing a suitable functional. Among ACMs, variational level set methods have been used to build an active contour with the aim of modeling arbitrarily complex shapes. Moreover, they can handle also topological changes of the contours. Self-Organizing Maps (SOMs) have attracted the attention of many computer vision scientists, particularly in modeling an active contour based on the idea of utilizing the prototypes (weights) of a SOM to control the evolution of the contour. SOM-based models have been proposed in general with the aim of exploiting the specific ability of SOMs to learn the edge-map information via their topology preservation property and overcoming some drawbacks of other ACMs, such as trapping into local minima of the image energy functional to be minimized in such models. In this survey, we illustrate the main concepts of variational level set-based ACMs, SOM-based ACMs, and their relationship and review in a comprehensive fashion the development of their state-of-the-art models from a machine learning perspective, with a focus on their strengths and weaknesses.

scholarly journals An Image Segmentation Method Based on Improved Regularized Level Set Model

2018 ◽  
Vol 8 (12) ◽  
pp. 2393 ◽  
Author(s):  
Lin Sun ◽  
Xinchao Meng ◽  
Jiucheng Xu ◽  
Shiguang Zhang
Keyword(s):  
Image Segmentation ◽  
Level Set ◽  
Energy Functional ◽  
External Energy ◽  
Regularization Term ◽  
Level Set Function ◽  
New Energy ◽  
Segmentation Approach ◽  
Set Function ◽  
Distance Regularization

When the level set algorithm is used to segment an image, the level set function must be initialized periodically to ensure that it remains a signed distance function (SDF). To avoid this defect, an improved regularized level set method-based image segmentation approach is presented. First, a new potential function is defined and introduced to reconstruct a new distance regularization term to solve this issue of periodically initializing the level set function. Second, by combining the distance regularization term with the internal and external energy terms, a new energy functional is developed. Then, the process of the new energy functional evolution is derived by using the calculus of variations and the steepest descent approach, and a partial differential equation is designed. Finally, an improved regularized level set-based image segmentation (IRLS-IS) method is proposed. Numerical experimental results demonstrate that the IRLS-IS method is not only effective and robust to segment noise and intensity-inhomogeneous images but can also analyze complex medical images well.

scholarly journals A Level Set Method in Shape and Topology Optimization for Variational Inequalities

2007 ◽  
Vol 17 (3) ◽  
pp. 413-430 ◽  
Author(s):  
Piotr Fulmański ◽  
Antoine Laurain ◽  
Jean-Francois Scheid ◽  
Jan Sokołowski
Keyword(s):  
Topology Optimization ◽  
Variational Inequalities ◽  
Shape Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Energy Functional ◽  
Optimization Techniques ◽  
Shape And Topology Optimization ◽  
And Topology ◽  
Topological Derivatives

A Level Set Method in Shape and Topology Optimization for Variational InequalitiesThe level set method is used for shape optimization of the energy functional for the Signorini problem. The boundary variations technique is used in order to derive the shape gradients of the energy functional. The conical differentiability of solutions with respect to the boundary variations is exploited. The topology modifications during the optimization process are identified by means of an asymptotic analysis. The topological derivatives of the energy shape functional are employed for the topology variations in the form of small holes. The derivation of topological derivatives is performed within the framework proposed in (Sokołowski and Żochowski, 2003). Numerical results confirm that the method is efficient and gives better results compared with the classical shape optimization techniques.

scholarly journals Dynamic Regulation of Level Set Parameters Using 3D Convolutional Neural Network for Liver Tumor Segmentation

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Zhuofu Deng ◽  
Qingzhe Guo ◽  
Zhiliang Zhu
Keyword(s):  
Neural Network ◽  
Convolutional Neural Network ◽  
Level Set ◽  
Liver Tumors ◽  
Window Size ◽  
Energy Functional ◽  
Tumor Segmentation ◽  
Dynamic Regulation ◽  
Low Contrast ◽  
3D Cnn

Segmentation of liver tumors plays an important role in the choice of therapeutic strategies for liver disease and treatment monitoring. In this paper, we generalize the process of a level set with a novel algorithm of dynamic regulation to energy functional parameters. The presented method is fully automatic once the tumor has been detected. First, a 3D convolutional neural network with dense layers for classification is used to estimate current contour location relative to the tumor boundary. Second, the output 3D CNN probabilities can dynamically regulate parameters of the level set functional over the process of segmentation. Finally, for full automation, appropriate initializations and local window size are generated based on the current contour position probabilities. We demonstrate the proposed method on the dataset of MICCAI 2017 LiTS Challenge and 3DIRCADb that include low contrast and heterogeneous tumors as well as noisy images. To illustrate the strength of our method, we evaluated it against the state-of-the-art methods. Compared with the level set framework with fixed parameters, our method performed better significantly with an average DICE improvement of 0.15. We also analyzed a challenging dataset 3DIRCADb of tumors and obtained a competitive DICE of 0.85±0.06 with the proposed method.

A Multi-Scale Information Fusion Level Set for Breast Tumor Segmentation

2021 ◽  
Vol 11 (8) ◽  
pp. 2062-2070
Author(s):  
Tongle Fan ◽  
Guanglei Wang ◽  
Yan Li ◽  
Zhongyang Wang ◽  
Hongrui Wang
Keyword(s):  
Level Set ◽  
Breast Tumor ◽  
Region Of Interest ◽  
Energy Functional ◽  
Surrounding Tissue ◽  
Tumor Segmentation ◽  
Energy Term ◽  
Edge Information ◽  
Breast Segmentation ◽  
Level Set Model

Purpose: Mammography is considered an effective method of examination in early breast cancer screening. Massive work by distinguished researchers of breast segmentation has been proposed. However, due to the blurry boundaries of the breast tumor, the variability of its shape and the overlap with surrounding tissue, the breast tumor’s accurate segmentation still is a challenge. Methods: In this paper, we proposed a novel level set model which based on the optimized local region driven gradient enhanced level set model (OLR-GCV) to segment tumor within a region of interest (ROI) in a mammogram. Firstly, Noise, labels and artifacts are removed from breast images. The ROI is then obtained using the intuitionistic fuzzy C-means method. Finally we used OLR-GCV method to accurately segment the breast tumor. The OLR-GCV model combines regional information, enhanced edge information and optimized Laplacian of Gaussian (LOG) energy term. The regional and enhanced edge information are used to capture local, global and gradient information of breast images. The optimized Laplacian of Gaussian (LOG) energy term is introduced in the energy functional to further optimize edge information to improve segmentation accuracy. Results: We evaluated our method on the MIAS and DDSM datasets. It yielded a Dice value of 96.86% on the former and 95.51% on the latter. Our method proposed achieves higher accuracy of segmentation than other State-of-the-art Methods. Conclusions: Our method has better segmentation performance, and can be used in clinical practice.

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